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The Quarterback Prediction Problem: Forecasting the Performance of College Quarterbacks Selected in the NFL Draft


Abstract and Figures

National Football League (NFL) teams spend substantial time and money trying to predict which college quarterbacks eligible to be drafted into the NFL will have successful professional careers. But despite this investment of resources, it is common for quarterbacks to perform much better or worse than anticipated. Prior work on this "quarterback prediction problem" has concluded that NFL teams are poor at determining which quarterbacks are likely to be successful based on information available prior to the draft. However, these analyses have generally focused only on quarterbacks who played in the NFL, ignoring those who were drafted but did not appear in a professional game. Using data on all quarterbacks drafted since 1997, we considered the problem of predicting NFL success as defined by two metrics (games played and Net Points), based on when a quarterback was drafted and his performances in college and at the NFL Combine. Our analyses suggest that college and combine statistics have little value for predicting whether a quarterback will be successful in the NFL. Contrary to previous work, we conclude that NFL teams aggregate pre-draft information-including qualitative observations-quite effectively, and their inability to consistently identify college quarterbacks who will excel in the professional ranks is a consequence of random variability in future performance due to factors which are unlikely to be observable.
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Submitted to the Annals of Applied Statistics
By Julian Wolfson, Vittorio Addonaand Robert H.
University of Minnesota, Macalester College, and University of
National Football League (NFL) teams spend substantial time
and money trying to predict which college quarterbacks eligible to
be drafted into the NFL will have successful professional careers. But
despite this investment of resources, it is common for quarterbacks to
perform much better or worse than anticipated. Prior work on this
“quarterback prediction problem” has concluded that NFL teams
are poor at determining which quarterbacks are likely to be success-
ful based on information available prior to the draft. However, these
analyses have generally focused only on quarterbacks who played in
the NFL, ignoring those who were drafted but did not appear in a
professional game. Using data on all quarterbacks drafted since 1997,
we considered the problem of predicting NFL success as defined by
two metrics (games played and Net Points), based on when a quar-
terback was drafted and his performances in college and at the NFL
Combine. Our analyses suggest that college and combine statistics
have little value for predicting whether a quarterback will be success-
ful in the NFL. Contrary to previous work, we conclude that NFL
teams aggregate pre-draft information – including qualitative obser-
vations – quite effectively, and their inability to consistently identify
college quarterbacks who will excel in the professional ranks is a con-
sequence of random variability in future performance due to factors
which are unlikely to be observable.
1. Introduction and Background. Quarterback is widely regarded
as the most important position on a professional football team. Finding a
good quarterback is difficult: In the National Football League (NFL), elite
quarterbacks are rarely available via trade or free agency, and hence are
Assistant Professor, Division of Biostatistics, University of Minnesota School of Public
Assistant Professor, Department of Mathematics, Statistics and Computer Science,
Macalester College
Research Scientist, Resuscitation Outcomes Consortium, University of Washington
Keywords and phrases: quarterback prediction problem, college football, NFL draft,
negative binomial regression
most often acquired via the amateur draft. Briefly, the draft is a mechanism
by which NFL teams select (in reverse order of their previous year’s winning
percentage) from a pool of eligible college players. Drafting a player gives
a team exclusive rights to negotiate a contract with that player. Though
players may be selected earlier or later in the draft for a variety of reasons,
a player’s draft position can generally be viewed as a team’s assessment of
his overall skill level.
Traditionally, quarterbacks command some of the largest contracts when
entering the NFL via the draft. When drafting a quarterback, teams must
therefore balance the substantial monetary investment required against the
expected benefit derived from the quarterback’s future performance. Given
the high stakes involved, teams have a vital interest in predicting how suc-
cessful an individual quarterback will be in the NFL. But in spite of the
enormous volume of information available about draft-eligible quarterback
prospects and the hundreds of person-hours spent assessing each player’s
abilities, it remains common for quarterbacks to perform dramatically better
or worse than anticipated. Several current or recent NFL starting quarter-
backs (e.g. Tom Brady, Matt Hasselbeck, Marc Bulger, Matt Cassel, Kyle
Orton, and David Garrard) were drafted in the fourth round or later, mean-
ing that at least 100 players, including a number of quarterbacks, were se-
lected before them. Others (e.g. Kurt Warner and Tony Romo) went un-
drafted entirely. Moreover, several quarterbacks selected with one of the
first five picks overall (e.g. JaMarcus Russell, Tim Couch, Akili Smith, Ryan
Leaf, and Heath Shuler) have played very poorly in the NFL. The challenge
of identifying college quarterback prospects who are most likely to succeed
at the professional level is among the “Hilbert Problems” for football iden-
tified by Schatz (2005). In the remainder of this paper, we will refer to this
challenge as the quarterback prediction problem.
The difficulty of predicting whether or not a college quarterback will be
successful in the NFL was highlighted in a 2008 New Yorker article by Mal-
colm Gladwell (Gladwell,2008). The article cited the work of Berri and
Simmons (2009), who concluded that the draft position of a quarterback
had a considerable impact on how much that quarterback played, but not
on how well he performed in the NFL. Quinn et al. (2007) arrived at similar
conclusions using different performance metrics. Lewin (2006) developed a
projection system for future NFL quarterbacks, and concluded that games
started and completion percentage in college were the only important pre-
dictors of later success, but did not provide the details of his methodology.
Massey and Thaler (2010) considered whether the compensation of draft
picks reflected their future performance, and concluded that teams were
overpaying early first-round draft picks.
If, as much of this work suggests, NFL teams are poor at identifying
college prospects who are likely to succeed as NFL quarterbacks, two possible
explanations are:
1. NFL teams may aggregate available information sub-optimally, em-
phasizing some attributes which do not correlate with NFL perfor-
mance, and de-emphasizing other attributes which are more predictive
of NFL success.
2. The variability in individual performance due to random, unmeasur-
able factors may make prediction inherently difficult, even if all avail-
able information were used optimally.
In this paper, we consider both of these explanations, and attempt to quan-
tify how much each contributes to the quarterback prediction problem. Our
work differs from previous research on this problem in two main ways. First,
we base our analyses on all quarterbacks drafted into the NFL, not only
on those who have played in at least one NFL game. Second, we explicitly
estimate the predictive ability of our models to assess the inherent difficulty
of the quarterback prediction problem.
Section 2describes the data, while Section 3introduces our outcome mea-
sures and predictors. Section 4provides details of the methods we employ.
In Section 5, we present the results of our analysis. We conclude with a brief
discussion in Section 6.
2. Data. Draft position and most NFL statistics were obtained from for all quarterbacks drafted since 1997. Num-
ber of sacks and fumbles lost were obtained from College statis-
tics back to the 2000-01 season were obtained from Career
college statistics for quarterbacks who played before 2000-01 were obtained
from several other sources, including school websites. The NFL Scouting
Combine is an annual week-long event held roughly two months prior to
draft day, during which college football players undergo a variety of physical
and mental evaluations at the request of NFL coaches, general managers,
and scouts. Physical evaluations from the combine were obtained from nfl-
In total, we obtained information on 160 quarterbacks. Brad Smith (who
played quarterback for Missouri and was drafted in the fourth round of
2006 by the New York Jets) and Isaiah Stanback (who played quarterback
for Washington and was drafted in the fourth round of 2007 by the Dallas
Cowboys) were omitted from our analysis because they have played almost
exclusively as wide receivers in the NFL.
The complete dataset is provided in the Supplementary Materials accom-
panying this paper.
3. Outcomes and predictors.
3.1. Outcomes. One fundamental challenge that arises in the quarter-
back prediction problem is how to quantify quarterback performance and
thereby determine how “successful” a quarterback’s professional career has
been. Cumulative statistics (e.g. games played/started, pass attempts/yards,
touchdowns etc.) are closely related to the number of opportunities given
to a quarterback, opportunities which may be determined by factors other
than on-field performance. For example, teams may be more reluctant to
replace a player who is performing poorly if that player was drafted early
(and hence highly paid); teams may be less tolerant of a poorly performing
player if he was selected later in the draft. Figure 1displays the number of
games played by quarterbacks drafted since 1997, stratified by the round in
which they were drafted.
1 2 3 4 5 6 7
0 50 100 150
Fig 1. Number of games played in the NFL by draft round
In order to avoid this potential problem with cumulative statistics, Berri
and Simmons (2009) quantified NFL performance by a variety of per-play
metrics, and concluded that a quarterback’s NFL performance was not as-
sociated with when he was selected in the draft. However, in most of their
analyses, quarterbacks with fewer than 100 plays of NFL experience were
excluded. Many of the excluded players had never been involved in a sin-
gle play in the NFL, and hence per-play metrics were undefined for these
Excluding quarterbacks with fewer than 100 plays from the analysis is
problematic unless one assumes that these quarterbacks would have per-
formed similarly, if given similar playing time, to those with more than 100
plays of experience. In other words, the results may be biased unless quar-
terbacks with fewer than 100 NFL plays are missing completely at random
(Little and Rubin,2002). But the missing completely at random (MCAR)
assumption seems tenuous: Once a college quarterback has been drafted onto
an NFL team, that team’s coaches can observe his performance in training
camp, team practices, and exhibition games before deciding whether or not
to allow him to play in a regular season game. While one might assert that
coaches and team personnel are beholden to draft status and other auxiliary
factors when making these decisions, an alternative explanation for Berri
and Simmons’ surprising findings is that they reflect selection bias. That is,
quarterback performance is unrelated to draft status conditional on an NFL
coach deeming a quarterback sufficiently skilled to play professionally, but
quarterbacks drafted in the earlier rounds are far more likely to possess this
minimum skill level and reach the 100-play threshold.
We would argue that NFL teams, as well as casual fans, are generally
interested in knowing whether one can predict the likelihood of NFL success
for all drafted quarterbacks before they play an NFL game. Indeed, draft
experts and fans often talk of a prospect’s “bust potential,” referring to the
possibility that a highly-touted college quarterback will be drafted early,
only to be judged incapable (presumably based on their performance in
practice and exhibition games) of playing at the NFL level. It is clearly of
interest to identify pre-draft information which might suggest that certain
quarterbacks are more or less likely to be “busts”.
For our analyses, we considered two cumulative statistics quantifying NFL
1. Games played. Counts the total number of NFL games in which a
quarterback has been involved in at least one play. In our analyses, we
treated games played as an integer-valued random variable, and also
considered three binary variants. Letting Gbe the number of games
played, we define
G(K)=(1 if GK
0 if G < K
for K= 1, 16, and 48. These cutoffs correspond, informally, to a min-
imal, moderate, and substantial degree of NFL success. Quarterbacks
with G1 (i.e. G(1) = 1) can be thought of as having reached a min-
imum competence threshold: their team’s coaching staff has judged
them good enough to play in an NFL game. Similarly, quarterbacks
with G(48) = 1 are generally considered very good to excellent, as few
poor quarterbacks are allowed to play in this many games (48 games
corresponds to three complete seasons).
2. Net Points. Berri and Simmons (2009) used a statistic, Net Points,
which quantifies how many points a quarterback contributes to his
team based on cumulative statistics. As per Berri (2008), Net Points
is calculated as
Net Points = 0.08*Yards - 0.21*Plays - 2.7*Interceptions -
where Yards = Passing Yards + Rushing Yards, and Plays = Pass At-
tempts + Rush Attempts + Sacks. Fractional Net Points are rounded
to the nearest integer. Berri and Simmons computed Net Points only
for quarterbacks who had accumulated statistics at the NFL level; for
our analysis, we assigned zero Net Points to quarterbacks who have not
played in the NFL, since they have not accumulated any of its com-
ponent statistics. Thirty quarterbacks had small negative Net Points
values (less than 10 in absolute value), which we set to zero. Figure 2
plots the distribution of Net Points.
Note that our outcome measures are defined for all drafted quarterbacks,
and may be affected by the number of playing opportunities that a quar-
terback is afforded. The degree to which playing opportunities depend on
factors other than on-field performance is unknown, but in Section 5, we
present analyses contradicting the view that these factors play a major role
in determining playing time for quarterbacks. We revisit this issue alongside
our conclusions in Section 6.
3.2. Predictors. We considered the following predictors of NFL perfor-
mance in our regression models: Draft position (Pick), year drafted (Year),
passing statistics compiled during a quarterback’s college career, and mea-
surements from the NFL Scouting Combine (including Height and Weight).
Net Points
0 500 1000 1500 2000
0 20 40 60 80 100 120
Fig 2. Histogram of Net Points in the NFL
In all our models, the Pick variable was log transformed. Table 1presents
summary statistics of the predictors in our analysis.
4. Methods.
4.1. Regression models. The binary variables G(1),G(16) , and G(48) were
modeled via logistic regression. Games played (G) was modeled via negative
binomial (NB) regression (Agresti,2002). Suppose that, given λ > 0, Yhas
a Poisson distribution with mean λ, and that λGamma(k, µ). Then the
marginal probability function of Yis negative binomial, taking the form
P(Y=y;k, µ) = Γ(y+k)
Γ(k)Γ(y+ 1) k
with E(Y) = µand var(Y) = µ+µ2/k.θ= 1/k reflects the degree of
overdispersion of the counts; as θ0, the negative binomial distribution
converges to the usual Poisson distribution. In our case, both games played
and Net Points showed evidence of overdispersion: the negative binomial
regression models we fit generally estimated θ2, with standard errors less
than 0.4.
Total N= 160
Predictor Median [Min, Max] # missing
ColGames 39 [12, 53] 19
Number of games played
CompPerc 58.7 [40.9, 70.4] 13
Completion percentage = (# Completions) / (# pass attempts)
YPA 7.7 [5.7, 10.1] 13
Yards per pass attempt = (Pass yards) / (# pass attempts)
Int 28 [1, 64] 15
Number of interceptions
TD 54 [0, 131] 11
Number of touchdowns
Height 75 [70, 79] 51
Height (in inches)
Weight 225 [192, 265] 51
Weight (in lbs.)
40-yard dash 48.1 [43.3, 53.7] 51
Time to run 40 yards (in 0.1s of a second)
Vertical jump 31.5 [21.5, 38.5] 79
Vertical leap height from a standing position (in inches)
Cone drill 71.3 [67.2, 78.0] 82
Time to run a course marked by cones (in 0.1s of a second)
Table 1
Summary statistics for predictors
As noted, quarterbacks could have zero Net Points either because they
did not play in the NFL and were assigned zero points by definition, or
because they did play and had their Net Points rounded to zero. Since zero
values for this outcome can be viewed as having been generated by two
separate processes, we modeled the Net Points outcome as a zero-inflated
negative binomial (ZINB) random variable (Greene,2008;Yau et al.,2003).
The ZINB model extends the NB model by allowing extra probability mass
to be placed on the value zero, with the probability that an observation is
a structural or “excess” zero modeled by logistic regression. Although it is
possible to use different predictors for the two components of a ZINB model,
we used the same sets of predictors for both components in our analysis.
For each regression, we considered two primary models. The first model
(Base) contained the college predictors (ColGames, CompPerc, YPA, Int,
and TD) listed in Table 1, along with Year; the second model contained
all the Base predictors plus log(Pick), a term accounting for where a player
was selected in the NFL draft. We also considered two secondary models
with the same predictors as the primary models, but excluding quarterbacks
selected in the first round. Due to the financial investment required to sign
first-round draft selections, one could reasonably argue that the playing
opportunities for these quarterbacks are most heavily influenced by external
factors unrelated to their on-field performance. An analysis which excludes
these players may indicate whether the predictors of success differ for more
“disposable” quarterbacks who were selected later in the draft and did not
command a large contract. Finally, we refit these four models using the
combine measurements (Height, Weight, 40-yard dash, Vertical jump, and
Cone drill) from Table 1in place of college statistics.
4.2. Assessing predictive accuracy. Predictions for each quarterback in
the dataset were generated based on the fitted models:
For the logistic regressions, predictions ˆ
iwere obtained as
with ˆπ(K)
irepresenting the estimated probability that G(K)
i= 1. For
the “Intercept only” model where ˆπ(K)is the same for all individuals,
predictions were derived via a biased coin-toss method, so that ˆ
was generated as a Bernoulli random variable with success probability
equal to ˆπ(K).
For the integer-valued outcomes, we label our predictions as ˆ
Yi, referring
either to predicted games played (NB models) or Net Points (ZINB models).
In the NB regressions, predictions ˆ
Yiwere obtained from the fitted
values for each individual i.
In the ZINB regressions, predictions were obtained for each individual
Yi=(0 if ˆ
θiif ˆ
where ˆ
φiis the estimated probability that individual irepresents a
structural zero, and ˆ
θiis the estimated mean for individual igiven
that he/she is not a structural zero.
Predictive accuracy for binary outcomes was quantified by the misclassi-
fication rate
MR =1
i|>0.5] ,
and predictive accuracy for integer-valued outcomes was quantified via the
absolute prediction error
AP E =1
where Yirefers to either games played or Net Points. Both the misclassi-
fication rate and absolute prediction error were estimated via 5-fold cross-
validation using the original data (Efron and Gong,1983).
5. Results.
5.1. Games played. Table 2reports the results of the eight regression
models, associated with the integer-valued games played variable Gde-
scribed in Section 4.1. The values in Table 2represent the percent increase
in the mean of G(and corresponding 95% confidence intervals) associated
with one-unit increases in each predictor. Tables 3,4, and 5give the percent
increases in the odds of P(G(K)= 1) (and corresponding 95% confidence
intervals) for K= 1, 16, and 48, respectively. Confidence intervals which
exclude zero are highlighted in bold.
All quarterbacks Rounds 2-7 only
Variable Base Base+Pick Base Base+Pick
ColGames 1 (-3,5) 1 (-3,5) 2 (-4,8) 2 (-3,7)
CompPerc 8 (0,15) 5 (-2,11) 4 (-4,13) 2 (-6,11)
YPA -6 (-34,35) -23 (-45,8) -28 (-55,18) -17 (-47,30)
Int 1 (-2,5) 0 (-3,3) 0 (-4,4) 0 (-2,2)
TD 0 (-2,2) 0 (-2,1) 0 (-2,3) 0 (-3,4)
Year -19 (-26,-11) -18 (-25,-11) -22 (-32,-11) -21 (-30,-10)
log(Pick) -33 (-43,-22) -47 (-71,-2)
Height 0 (-22, 28) 1 (-20, 28) -12 (-35, 19) -4 (-30, 31)
Weight 1 (-3, 5) 0 (-3, 4) 0 (-4, 4) 0 (-4,4)
40-yard dash 5 (-21, 45) -1 (-25, 33) 12 (-28, 70) 3 (-33,56)
Vertical jump 4 (-10, 22) -1 (-13, 14) 6 (-13, 28) 1 (-17, 22)
Cone drill 0 (-15, 19) 11 (-6, 32) 14 (-7, 40) 16 (-5, 42)
Year -20 (-31,-9) -22 (-32,-11) -21 (-34, -5) -23 (-36,-8)
log(Pick) -37 (-54,-16) -47 (-73,11)
Table 2
Percent change in number of NFL games played (with 95% confidence intervals)
associated with one-unit differences in college and combine statistics, year drafted, and
draft position.
Year was negatively associated with games played in nearly all models;
predictably, more years in the league generally leads to more games played.
The only other predictor which was consistently associated with games
All quarterbacks Rounds 2-7 only
Variable Base Base+Pick Base Base+Pick
ColGames 0 (-6, 6) 0 (-6, 7) 2 (-5, 9) 1 (-6, 8)
CompPerc 3 (-8, 17) -1 (-13, 13) 1 (-11, 14) -1 (-13, 13)
YPA 36 (-29, 172) 33 (-33, 171) 27 (-36, 157) 32 (-33, 169)
Int 2 (-3, 8) 1 (-4, 7) 1 (-4, 7) 1 (-4, 7)
TD 0 (-3, 3) 0 (-3, 3) 0 (-3, 3) 0 (-3, 3)
Year -19 (-32, -4) -21 (-36, -4) -21 (-36, -5) -21 (-36, -4)
log(Pick) -75 (-91, -47) -68 (-90, -13)
Height -2 (-38, 54) 4 (-36, 71) -2 (-40, 58) 3 (-37, 69)
Weight 3 (-4, 11) 2 (-6, 10) 2 (-5, 10) 2 (-6, 10)
40-yard dash 3 (-35, 72) -2 (-42, 70) -6 (-45, 65) -5 (-45, 68)
Vertical jump 5 (-17, 32) -1 (-22, 26) 0 (-23, 27) -2 (-23, 26)
Cone drill 1 (-23, 32) 9 (-17, 45) 5 (-19, 39) 9 (-18, 45)
Year -10 (-29, 13) -15 (-35, 10) -13 (-34, 11) -15 (-35, 10)
log(Pick) -65 (-90, -19) -56 (-88, 39)
Table 3
Percent change in odds of playing 1NFL game (with 95% confidence intervals)
associated with one-unit differences in college and combine statistics, year drafted, and
draft position.
All quarterbacks Rounds 2-7 only
Variable Base Base+Pick Base Base+Pick
ColGames 1 (-4, 7) 1 (-5, 8) 2 (-5, 9) 0 (-7, 8)
CompPerc 7 (-4, 19) 4 (-7, 17) 3 (-9, 16) 1 (-11, 15)
YPA -5 (-45, 64) -27 (-62, 39) -25 (-62, 43) -22 (-61, 54)
Int 0 (-4, 5) -1 (-6, 5) 0 (-5, 6) 0 (-5, 6)
TD 1 (-1, 4) 1 (-2, 4) 1 (-2, 4) 1 (-2, 4)
Year -21 (-33, -10) -26 (-39, -12) -21 (-35, -5) -19 (-34,-3)
log(Pick) -62 (-76, -45) -65 (-86,-15)
Height 22 (-20, 90) 37 (-14, 128) 4 (-35, 69) 20 (-29, 109)
Weight 0 (-7, 6) -3 (-9, 4) -1 (-7, 6) -3 (-10, 5)
40-yard dash -9 (-42, 40) -19 (-50, 32) -10 (-49, 56) -14 (-54, 58)
Vertical jump 2 (-17, 27) -3 (-23, 21) 0 (-22, 28) -4 (-26, 24)
Cone drill 14 (-11, 48) 31 (-1, 77) 26 (-4, 71) 36 (1, 89)
Year -27 (-43, -10) -34 (-51, -16) -25 (-44, -4) -29 (-49, -7)
log(Pick) -60 (-82, -28) -75 (-95, -8)
Table 4
Percent change in odds of playing 16 NFL games (with 95% confidence intervals)
associated with one-unit differences in college and combine statistics, year drafted, and
draft position.
played was draft position (with quarterbacks drafted in the later rounds
playing fewer games). The influence of draft status was relatively consistent
across models: one log differences in draft pick number (eg. the difference
between the first overall selection and the third, or the tenth overall se-
lection and the twenty-seventh) were associated with 30-60% fewer games
All quarterbacks Rounds 2-7 only
Variable Base Base+Pick Base Base+Pick
ColGames 10 (1,21) 14 (2, 29) 18 (0,49) 16 (-3,46)
CompPerc 16 (0,37) 25 (4, 56) 34 (3,86) 34 (3,88)
YPA -33 (-71,47) -72 (-91,-23) -73 (-95,2) -72 (-94,14)
Int -1 (-8,6) -2 (-11,8) 0 (-15,16) -1 (-17,16)
TD 0 (-3,4) -2 (-7,3) -4 (-13,3) -4 (-13,4)
Year -38 (-52,-23) -45 (-61,-28) -56 (-79,-29) -53 (-78,-25)
log(Pick) -65 (-80,-45) -59 (-94,140)
Height 38 (-28, 181) 28 (-37, 173) 5 (-52, 133) 40 (-42, 284)
Weight 6 (-3, 18) 8 (-4, 25) 6 (-5, 21) 6 (-7, 23)
40-yard dash -3 (-53, 77) -4 (-56, 84) 43 (-40, 258) 39 (-54, 362)
Vertical jump 2 (-28, 43) -7 (-39, 38) 7 (-30, 67) -3 (-49, 69)
Cone drill -8 (-40, 38) -1 (-40, 62) -13 (-47, 41) -14 (-52, 46)
Year -45 (-67, -19) -51 (-74, -24) -32 (-63, 9) -37 (-69, 5)
log(Pick) -58 (-82, -21) -87 (-99, 11)
Table 5
Percent change in odds of playing 48 NFL games (with 95% confidence intervals)
associated with one-unit differences in college and combine statistics, year drafted, and
draft position.
played and similar decreases in the odds of achieving the previously defined
games played thresholds. Neither college nor combine statistics were asso-
ciated with number of games played, playing in 1, or playing in 16
NFL games. However, completion percentage and number of games played
in college were positively associated with playing in 48 games in the NFL,
even after adjusting for draft status.
Models fitted to quarterbacks drafted after the first round yielded gen-
erally similar results to models fitted to all drafted quarterbacks. The only
notable differences between models including and excluding first-round quar-
terbacks were for G(48), the indicator of playing at least 48 NFL games.
For G(48), confidence intervals for College Games, YPA, Year and log(Pick)
excluded zero in models using all quarterbacks but included zero when first-
round picks were omitted. However, the point estimates for these covariates
did not change substantially.
5.2. Net Points. Table 6summarizes the results of the NB count por-
tions of the ZINB models for Net Points, as before, reporting percent in-
creases in the mean for a one-unit increase in each predictor, along with
95% confidence intervals. For the sake of brevity, we do not report coeffi-
cient estimates from the “excess zeros” portions of the ZINB models. Briefly,
log(Pick) attained significance in all of these models, with later selections
having a higher chance of being a zero. Faster cone drill times were associ-
ated with a higher probability of being zero in two of the four models. No
other combine measure or college statistic, nor year drafted, was associated
with the probability of being an excess zero.
All quarterbacks Rounds 2-7 only
Variable Base Base+Pick Base Base+Pick
ColGames 3 (-2,8) 2 (-2,7) 2 (-8,14) -1 (-11,10)
CompPerc 11 (1,21) 9 (1,17) 1 (-11,15) -1 (-13,13)
YPA -14 (-44,32) -36 (-59,-2) -61 (-80,-23) -72 (-87,-38)
Int 1 (-4,6) 1 (-3,5) -1 (-7,6) -1 (-8,7)
TD -1 (-3,2) -1 (-3,1) 1 (-3,4) 2 (-2,7)
Year -20 (-28,-11) -20 (-28,-12) -28 (-41,-11) -28 (-42,-11)
log(Pick) -27 (-39,-14) 53 (-42,309)
Height -12 (-32, 15) -9 (-29, 18) -26 (-49, 7) -21 (-48, 20)
Weight 5 (1, 10) 4 (0, 8) 5 (0, 10) 4 (-1, 9)
40-yard dash 6 (-28, 56) 6 (-26, 53) 61 (-20, 225) 53 (-22, 199)
Vertical jump -8 (-24, 12) -9 (-23, 9) 8 (-22, 49) 6 (-22, 43)
Cone drill -10 (-24, 8) -2 (-18, 17) -3 (-25, 24) -2 (-24, 26)
Year -27 (-38, -14) -27 (-38, -15) -23 (-41, 0) -23 (-41, -1)
log(Pick) -24 (-43, 1) -25 (-71, 93)
Table 6
Percent change in NFL Net Points (with 95% confidence intervals) associated with
one-unit differences in college and combine statistics, year drafted, and draft position.
Generally, the conclusions for Net Points are very similar to those for
NFL games played: Year and draft position were negatively associated with
Net Points (i.e. quarterbacks drafted more recently and later in the draft
produced fewer Net Points), and college/combine statistics were generally
not associated with this outcome. The one exception to this rule was YPA,
which was negatively associated with Net Points in three of the four models
in which it was incorporated, including both models adjusting for draft po-
sition. We note, however, that the direction of this relationship is contrary
to conventional wisdom (which would dictate that quarterbacks with higher
college YPA will tend to have more success in the NFL). We discuss the
interpretation of this counter-intuitive result in Section 6.
As with games played, models for Net Points fitted to all quarterbacks
did not differ greatly from models fitted to quarterbacks drafted in rounds
2-7. Point estimates for the (negative) effect of YPA on Net Points were
larger in magnitude for models excluding first-round quarterbacks, as were
estimates of the (positive) effect of 40-yard dash time, although the very
wide confidence intervals for the latter should be noted.
5.3. Predictive accuracy. We compared the predictive performance of
nine models:
1. Intercept only: A naive model which uses no predictor information,
estimating a common intercept term for the entire population.
2. Year: A model including draft year as the sole predictor.
3. + log(Pick): A model including Year and log(Pick).
4. + College Stats: A model including Year and the college statistics
listed in Table 1.
5. + Combine Stats: A model including Year and the combine statistics
listed in Table 1.
6. + College + Combine: A model including Year, and college and
combine statistics.
7. + log(Pick) + College: A model including Year, log(Pick), and
college statistics.
8. + log(Pick) + Combine: A model including Year, log(Pick), and
combine statistics.
9. + log(Pick) + College + Combine: A model including all of the
available predictors.
Figure 3summarizes the misclassification rate estimates for G(1), G(16),
and G(48) from 100 runs of 5-fold cross-validation. Results (not shown) were
similar when first-round picks were excluded from the analysis.
From Figure 3, we observe that, for G(1), the model containing only infor-
mation on what year a quarterback was drafted had the smallest misclassifi-
cation rate. For G(16) and G(48), the model which additionally incorporated
information on a quarterback’s draft position performed best. College and
combine measurements provided no additional predictive value beyond Year
and Pick; all the models including college and combine statistics misclassi-
fied quarterbacks at a higher rate than the simpler models. Indeed, these
models generally offered no improvement in misclassification rate over mod-
els with Year as the sole predictor. The model including college and combine
statistics but not log(Pick) (sixth row, for each of G(1),G(16), and G(48) , in
Figure 3) had worse classification performance than all but the naive Inter-
cept Only model.
Figures 4and 5summarize the cross-validation estimates (based on 100
runs of 5-fold cross-validation) of the absolute prediction error for games
played and Net Points, respectively. As with the binary outcomes, results
were similar when quarterbacks drafted in the first round were excluded
from the analysis.
For the integer-valued games played outcome, models with Year and Year
+ log(Pick) appeared to predict slightly better than the Intercept Only
model, and models incorporating college and combine statistics performed
substantially worse. The decrease in prediction error due to including Year
and log(Pick) was greater for the Net Points outcome, while the models
using college and combine statistics did not seem to yield better prediction
of Net Points than the Intercept Only model.
6. Discussion. Based on the preceding analyses, we draw the following
NFL teams appear to use pre-draft information intelligently. Year
drafted and draft position were by far the most important predictors of fu-
ture NFL success. We found some evidence that quarterbacks with higher
college YPA are likely to produce fewer Net Points in the NFL, indicating
that NFL teams may be drafting college quarterbacks with high YPA earlier
than their talent level would dictate. YPA may be inflated for quarterbacks
who play at large colleges with elite surrounding talent or in systems de-
signed to emphasize the passing game. But, overall, it does not appear that
NFL teams are systematically under- or over-emphasizing particular quan-
titative measures.
Our results also suggest that draft position provides information not
contained in college and combine statistics. This is not surprising, since
NFL teams possess a plethora of qualitative information on quarterback
prospects not related to in-game performance. For example, reports on
player attributes compiled by professional scouts, observations obtained at
“Pro Days” organized by individual colleges and universities, knowledge of
how strength of college opponents/teammates (or the “system” in which
the quarterback played) may have affected traditional statistics, injury sta-
tus, and personal interactions may all provide crucial knowledge to an NFL
A competing interpretation of our results is that NFL teams are using
pre-draft information sub-optimally and reinforcing these decisions by sys-
tematically denying or awarding playing time to quarterbacks based on their
draft position without regard to on-field performance. Previous work has fo-
cused on this possibility, but the resulting approach (considering per-play
data, and thereby excluding quarterbacks who have not played in the NFL)
is vulnerable to selection bias, which may be severe in this case. In our anal-
yses, we chose to consider outcomes which are dependent on the amount
of playing time a quarterback is given. We investigated the plausibility of
the hypothesis that playing time is awarded to highly-drafted quarterbacks
without regard to performance by fitting models which excluded quarter-
backs drafted in the first round, precisely those one would expect to benefit
most from a policy of awarding opportunities based on status rather than
merit. Neither the effect of draft position nor any of the other predictors we
considered was appreciably different in the analyses of this subset of quar-
terbacks. Though this finding does not rule out the possibility that external
factors influence playing time decisions, it suggests that the role of such fac-
tors may be exaggerated.
College and combine statistics for drafted quarterbacks are not
reliably associated with, or predictive of, success in the NFL.
In sports statistics circles, much has been made about a projection sys-
tem (Lewin,2006) for quarterbacks which uses the number of games started
in college and college completion percentage to predict future NFL suc-
cess. In our analyses, these variables were only associated with an indicator
of playing at least 48 NFL games, but they were not related to any of our
other outcome measures. Generally, college and combine performance statis-
tics provided no additional predictive ability beyond year drafted and draft
position. Indeed, in most cases, including college/combine measurements
degraded predictive performance, suggesting that the amount of statistical
noise in these predictors overwhelms any predictive value they might have.
The quarterback prediction problem is inherently difficult. Though
it appears that NFL teams do have some ability to discriminate between
quarterbacks who are likely to be successful in the NFL and those who are
not, there remains substantial uncertainty in predicting the future perfor-
mance of college quarterback prospects. Even the best-performing predictive
model for the indicator of playing at least 16 NFL games had a misclassifica-
tion rate over 30%. Similarly, the smallest estimated prediction error for the
integer-valued games played outcome was nearly 20 games, over one seasons’
worth. The smallest estimated prediction error for Net Points was greater
than 125 points, a threshold achieved by fewer than 30% of the quarterbacks
in our dataset.
Given the poor predictive performance of models incorporating a variety
of quantitative measures, it seems unlikely that collecting more statistics on
the performance of college quarterbacks will yield a clearer picture about
their likelihood of success in the NFL. Indeed, one might reasonably ar-
gue that there are few observable factors, either quantitative or qualitative,
which are not already being used in a near-optimal way to predict quar-
terback performance. Though NFL draft “experts” at the major sports net-
works may object, it appears that factors which are inherently unmeasurable
and/or random play a major role in determining whether a quarterback will
succeed at the professional level.
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Corresponding author:
Julian Wolfson
Division of Biostatistics
School of Public Health
University of Minnesota
A460 Mayo Building,
MMC 303
420 Delaware St. S.E.
Minneapolis, MN 55455
0.1 0.2 0.3 0.4 0.5
Misclassification rate
Intercept only
+ log(Pick)
+ College Stats
+ Combine Stats
+ College + Combine
+ log(Pick) + College
+ log(Pick) + Combine
+ log(Pick) + College + Combine
0.1 0.2 0.3 0.4 0.5 0.6
Misclassification rate
Intercept only
+ log(Pick)
+ College Stats
+ Combine Stats
+ College + Combine
+ log(Pick) + College
+ log(Pick) + Combine
+ log(Pick) + College + Combine
0.0 0.1 0.2 0.3 0.4
Misclassification rate
Intercept only
+ log(Pick)
+ College Stats
+ Combine Stats
+ College + Combine
+ log(Pick) + College
+ log(Pick) + Combine
+ log(Pick) + College + Combine
Fig 3. Misclassification rates from 100 runs of 5-fold cross-validation
10 20 30 40 50 60 70 80
Absolute prediction error
Intercept only
+ log(Pick)
+ College Stats
+ Combine Stats
+ College + Combine
+ log(Pick) + College
+ log(Pick) + Combine
+ log(Pick) + College + Combine
Fig 4. Absolute prediction error estimates for NFL games played from 100 runs of 5-fold
50 100 200 500 1000
Absolute prediction error
Intercept only
+ log(Pick)
+ College Stats
+ Combine Stats
+ College + Combine
+ log(Pick) + College
+ log(Pick) + Combine
+ log(Pick) + College + Combine
Fig 5. Absolute prediction error estimates for Net Points from 100 runs of 5-fold cross-
... However, it is also critical to enhance scouting methodology to indicate players' "bust potential." Bust potential is the potential of a highly anticipated college player being incapable of performing at an anticipated level of play once drafted into the NFL (28). The need for improved player scouting is also supported by research which indicate that the top NFL Draft picks are overvalued (2,13). ...
... Quarterbacks can improve their scouting value with enhancement of future performance indicators (e.g., taller, smarter, faster) (2,6). Results of the current research study validate Wolfson's et al. (28) findings for QBs' average height of 75 in. ...
... Proper weight management is essential to ensure for a prolonged career; if a player is underweight for their respected position, it will increase the risk of injury (9). The results of the current research study validate Wolfson's et al. (28) findings for QB's average weight of 225 lb (102.06 kg.). ...
Fitzgerald, CF and Jensen, RL. A Comparison of the National Football League's annual National Football League combine 1999-2000 to 2015-2016. J Strength Cond Res XX(X): 000-000, 2018-The purpose of this study was to determine if elite football players are becoming bigger, faster, and stronger over the past decade by analyzing individual performances at the National Football League's (NFL) Combine. This study was conducted with (N = 1,263) subjects from the 1999-2000 (99-00) NFL Combines (n = 635) and the 2015-2016 (15-16) NFL Combines (n = 628) separated by position. Data were collected for height, weight, 40-yd (36.58 m) dash, NFL 225 lb. (102.06 kg) repetitions test, vertical jump (VJ), broad jump (BJ), pro-agility shuttle, and 3-cone drill. Statistical significance between the years for all subjects participating in the NFL Combine was found for the 40-yd dash (99-00: mean ± SD = 4.85 ± 3.2; 15-16: 4.80 ± 3.5; p = 0.002) and VJ (99-00 = 32.30 ± 4.08; 15-16: 32.86 ± 4.17; p = 0.028) at the alpha p < 0.05 level. Statistical significance was also found for BJ (99-00 = 111.37 ± 8.81; 15-16: 115.03 ± 9.22; p < 0.001) and the 3-cone drill (99-00 = 7.41 ± 0.42; 15-16: 7.29 ± 4.1; p < 0.001) at the alpha p < 0.001 level. There were no statistically significant findings (p > 0.05) for weight or height found across all subjects by combine years. Results indicate that elite football players have improved their performance, when comparing results from 1999-2000 to 2015-2016. These finding may be beneficial to NFL franchises in their prospective player assessments.
... Wolfson et al. [1] addressed the backward prediction problem. Their analysis showed that college and combine statistics have little value in predicting whether a quarterback will Recent examinations clearly and unambiguously have shown that sum of ranking differences (SRD) realizes a multicriteria decision making (MDCM) tool [6,7]. ...
Full-text available
Predicting the success of National Football League drafts has always been an exciting issue for the teams, fans and even for scientists. Among the numerous approaches, one of the best techniques is to ask the opinion of sport experts, who have the knowledge and past experiences to rate the drafts of the teams. When asking a set of sport experts to evaluate the performances of teams, a multicriteria decision making problem arises unavoidably. The current paper uses the draft evaluations of the 32 NFL teams given by 18 experts: a novel multicriteria decision making tool has been applied: the sum of ranking differences (SRD). We introduce a quick and easy-to-follow approach on how to evaluate the performance of the teams and the experts at the same time. Our results on the 2021 NFL draft data indicate that Green Bay Packers has the most promising drafts for 2021, while the experts have been grouped into three distinct groups based on the distance to the hypothetical best evaluation. Even the coding options can be tailored according to the experts’ opinions. Statistically correct (pairwise or group) comparisons can be made using analysis of variance (ANOVA). A comparison to TOPSIS ranking revealed that SRD gives a more objective ranking due to the lack of predefined weights.
... Nearly all previous studies that examined NFL quarterback performance attempted to project performance using only variables known to teams before quarterbacks were drafted (e.g., see Berri & Simmons, 2011;Cook et al., 2020;Craig & Winchester, 2021;Hendricks et al., 2003;Kitchens, 2015;Kuzmits & Adams, 2008;Mirabile, 2005;Pitts & Evans, 2018;Rosen & Olbrecht, 2020;and Wolfson et al., 2011). Thus, these studies were primarily interested in how NFL teams could identify talented players in the draft. ...
The authors examined whether incumbent starting quarterbacks in the National Football League (NFL) performed better after their teams drafted another quarterback in the first round of the preceding draft. There was some evidence that quarterbacks exhibited slightly improved performance under these conditions. However, the impact on performance was small. There was little evidence of opportunistic behavior by quarterbacks, but quarterbacks may perform slightly better in the first year of a new contract. The authors conclude that quarterbacks are already exerting at or near their maximum effort level and thus their performances are unlikely to be greatly impacted by dismissal threats or contract details.
... However, when Wolfson et al. (2011) attempted a similar study on quarterbacks, they found that "College and combine statistics have little value." The problem was not that NFL teams sub-optimally collect qualitative and quantitative data. ...
Full-text available
Quarterback performance can be difficult to rank, and much effort has been spent in creating new rating systems. However, the input statistics for such ratings are subject to randomness and factors outside the quarterback's control. To investigate this variance, we perform a sensitivity analysis of three quarterback rating statistics: the Traditional 1971 rating by Smith, the Burke, and the Wages of Wins ratings. The comparisons are made at the team level for the 32 NFL teams from 2002-2015, thus giving each case an even 16 games. We compute quarterback ratings for each offense with 1-5 additional touchdowns, 1-5 fewer interceptions, 1-5 additional sacks, and a 1-5 percent increase in the passing completion rate. Our sensitivity analysis provides insight into whether an elite passing team could seem mediocre or vice versa based on random outcomes. The results indicate that the Traditional rating is the most sensitive statistic with respect to touchdowns, interceptions, and completions, whereas the Burke rating is most sensitive to sacks. The analysis suggests that team passing offense rankings are highly sensitive to aspects of football that are out of the quarterback's hands (e.g., deflected passes that lead to interceptions). Thus, on the margins, we show arguments about whether a specific quarterback has entered the elite or remains mediocre are irrelevant.
... The majority of prior studies on the subject consider the impact of various factors related to a player's collegiate career on either draft position, NFL productivity or both. There is evidence that collegiate productivity, speed, height, body mass index (BMI) and variables measuring a player's performance in various NFL combine drills are significant predictors of when a player will be selected in the NFL draft and, to a lesser extent, his NFL productivity (Treme and Allen 2009;Berri and Simmons 2011;Wolfson, Addona, and Schmicker 2011;Mulholland and Jensen 2014;Weir and Wu 2014). In these studies, NFL productivity is typically measured by number of games played, number of games started and position specific statistics such as passing yards, net points (see Berri, Schmidt, and Brook 2006) or approximate value. ...
Employing data on National Football League (NFL) quarterbacks drafted between 2002 and 2012, the authors consider whether factors correlated with a quarterback being more productive in the NFL are the same factors that correlate with an improved draft position. In particular, the authors consider the relevance of scores on the Wonderlic test. Contrary to all prior literature on the subject, the authors find that performance on the Wonderlic test is positively correlated with NFL performance. However, the authors find no clear evidence that Wonderlic scores are correlated with draft position. Beyond this primary finding, the authors reveal many other interesting results that should help researchers better understand a quarterback’s progression from college to the NFL.
... For example, it is common for talent identification practices to include anthropometric measures, however children can undergo a number of growth spurts during puberty making fully-matured measurement outcomes difficult to predict (1,10,38). In addition, the skill and subjective approach of coaches is variable, the definition of talent can be lacking, and the translation of individual performance results to team success difficult to quantify (10,28,38,50). Talent Identification becomes more subjective in elite players as the difference between performance scores reduces and the relative influence of the typical error of each physical test increases (2,28). ...
Traditional talent identification relies on physical performance tests to select athletes. As players gain experience, the sensitivity of these tests in differentiating between player ability is reduced which can lead to an over-reliance on qualitative parameters and subjective selection. Using rugby union as an example, and using sample test results from the literature, this theoretical paper builds on related work by adding a number of sport-specific predictor variables (relative age, genetics, psychology and situational awareness) applied with weighting constants to forecast performance. By normalising and amalgamating test scores a single talent index was achieved and an iterative technique to fine-tune the variables and weightings proposed. The paper demonstrates how to differentiate player talent in-practice, when for example based on sprint results the sub-elite players appear to out-class the elite. This hypothetical algorithm could be used to highlight quantitative differences and better rank elite and sub-elite players in a variety of scenarios.
We use college football data and, in some cases, ESPN scout grades to estimate (1) attributes that are likely to result in a college quarterback being selected by a National Football League (NFL) team, and (2) the performance of rookie quarterbacks in the NFL. We find that both college passing and rushing ability are significantly correlated with NFL selection, with strong passing ability the most important trait for making the NFL. Among quarterbacks selected for the NFL, college rushing ability is significantly correlated with NFL performance, but college passing ability is not. College rushing ability is also a significant determinant of NFL performance when scout grades are included as an explanatory variable. We conclude that rushing prowess is the key determinant of the NFL success of quarterbacks with sufficient passing skills to warrant NFL selection. Our findings also indicate that scouts systematically undervalue rushing ability when assessing the NFL potential of college quarterbacks.
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Many factors are considered when making a hiring decision in the National Football League (NFL). One difficult decision that executives must make is who they will select in the offseason. Mathematical models can be developed to aid humans in their decision-making processes because these models are able to find hidden relationships within numeric data. This research proposes the H euristic E valuation of A rtificially R eplaced T eammates (HEART) methodology, which is a mathematical model that utilizes machine learning and statistical-based methodologies to aid managers with their hiring decisions. The goal of HEART is to determine expected and theoretical contribution values for a potential candidate, which represents a player’s ability to increase or decrease a team’s forecasted winning percentage. In order to validate the usefulness of the methodology, the results of a 2007 case study were presented to subject matter experts. After analyzing the survey results statistically, five of the eight decision-making categories were found to be “very useful” in terms of the information that the methodology provided.
We show that firms can employ data‐driven methods to improve their hiring decisions. Specifically, we use data available to National Football League (NFL) teams prior to the NFL draft to estimate econometric models that predict the future performance of drafted quarterbacks. As our methods are replicable, stakeholders can use them to improve the draft's efficiency and help it accomplish its mission to promote competitive balance. Furthermore, data‐driven methods such as ours can help firms avoid biases against employee characteristics that do not affect future job performance. (JEL L83)
The National Football League (NFL) Scouting Combine takes place annually for the purpose of allowing NFL teams to evaluate prospects. The battery of six physical tests receives a great deal of attention, and are a focus of team personnel as well as fans of NFL teams. Recently, some have suggested that the current battery of tests should be modified. This work aims to characterize the multivariate dependence structure between tests for Combine prospects, for both typical and elite-level performers, for the purpose of better understanding the current battery of tests before making modifications. Through analysis of two pairwise dependence matrices, one quantifying dependence in the center of the distribution and the other quantifying dependence in the tails of the distribution, this analysis finds that several events show differing levels of association, and that fewer Combine events may be sufficient going forward.
Full-text available
We present several modifications of the Poisson and negative binomial models for count data to accommodate cases in which the number of zeros in the data exceed what would typically be predicted by either model. The excess zeros can masquerade as overdispersion. We present a new test procedure for distinguishing between zero inflation and overdispersion. We also develop a model for sample selection which is analogous to the Heckman style specification for continuous choice models. An application is presented to a data set on consumer loan behavior in which both of these phenomena are clearly present.
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Seventy quarterbacks were selected during six NFL drafts held 1999-2004. This paper analyzes information available prior to the draft (college, college passing statistics, NFL Combine data) and draft outcomes (overall number picked and signing bonus). Also analyzed for these players are measures of NFL playing opportunity (games played, games started, pass attempts) and measures of productivity (Pro Bowls made, passer rating, DVOA, and DPAR) for up to the first seven years of each drafted player’s NFL career. We find that more highly-drafted QBs get significantly more opportunity to play in the NFL. However, we find no evidence that more highly-drafted QBs become more productive passers than lower-drafted QBs that see substantial playing time. Furthermore, QBs with more pass attempts in their final year of more highly-ranked college programs exhibit lower NFL passing productivity.
In The Numbers Game, Alan Schwartz details the history of player performance measures in professional baseball. Soon after players took the field for professional teams in the 19th century people began to track such measures as hits and at-bats. And in 1870, H.A. Dobson noted that a baseball player’s efficiency could be measured simply with batting average - calculated simply by dividing hits by at-bats. As time went by increasingly sophisticated metrics were developed, such as on-base percentage, slugging percentage, OPS (on-base percentage plus slugging average), among others. Tracking the statistics and developing new metrics does require the expenditure of some effort. Is there a benefit generated to offset this cost? The answer to this query begins with why player statistics are tracked in the first place. For any game we can see which team won and which team lost by looking at the scoreboard. The question we have is which players on each team were primarily responsible for the outcome we observe. To get at this question, interested observers, i.e., teams, the media, fans, analyze player statistics. The purpose behind this effort is to separate each player from his team and connect that specific player’s actions accurately to the team outcome observed. There are two reasons why we wish to separate the player from his team. First, we wish to explain why a specific team has won or lost. Specifically, which players are most responsible for the outcome we observed? From the team’s perspective, though, there is a more important issue. Teams need to know which players to employ in the future. By tracking and analyzing player statistics teams hope to identify the players who will help the team be successful in the future. In sum, statistics are tracked to both explain what we observed in the past and determine what actions a team should take in the future. In baseball the first task is relatively easy. The statistics tracked for baseball play-ers - singles, doubles, triples, home runs, etc. - are clearly linked to runs scored and wins. And understanding the value of these statistics is fairly easy. One does not need advanced regression analysis to understand that one more home run is worth more to a team than one more single. As noted in Berri, Schmidt, and Brook (2006), baseball performance is not entirely consistent across time. So forecasting future performance in baseball is somewhat difficult, even if one completely understands the data collected. Basketball also has an abundance of player statistics. Teams track for each player points, rebounds, steals, assists, and other factors to help decision-makers both explain and predict performance. Relative to baseball, the explanation of why teams win and lose is a bit more difficult in basketball. After all, which is more important, an additional point scored or an assist? Would a team rather have one more rebound or one more blocked shot? As noted in Berri et al. (2006), with a bit of thought one can untangle the relative value of these statistics. Furthermore, relative to baseball, players in basketball tend to be more consistent across time. Hence, player forecasts are relatively more reliable in hoops. What about the American football? Yes, a number of statistics are tracked. But statistics are only commonly tracked for certain positions. Quarterbacks and running backs each have a number of factors tracked and these clearly can be used to assess performance. Other positions, though, such as offensive lineman, have hardly any statistics. Still, numbers do exist in football. The purpose of this essay is to explore how these statistics can be used to explain past performance, as well as predict the future. In other words, do statistics in the National Football League (NFL) have the same value as statistics tracked in baseball and basketball?
This is an invited expository article for The American Statistician. It reviews the nonparametric estimation of statistical error, mainly the bias and standard error of an estimator, or the error rate of a prediction rule. The presentation is written at a relaxed mathematical level, omitting most proofs, regularity conditions, and technical details.
The reverse order college draft gives the worst teams in the National Football League (NFL) the opportunity to hire the best amateur talent. For it to work effectively, teams must be able to identify the “best” talent. Our study of NFL quarterbacks highlights problems with the draft process. We find only a weak correlation between teams’ evaluations on draft day and subsequent quarterback performance in the NFL. Moreover, many of the factors that enhance a quarterback’s draft position are unrelated to future NFL performance. Our analysis highlights the difficulties in evaluating workers in the uncertain environment of professional sports. KeywordsQuarterback–College–Draft–Performance
David Hilbert was a mathematician who in 1900 delivered the most influential speech in the history of mathematics (Hilbert 1902). He outlined 23 major problems to be studied in the next century, while outlining a philosophy for how mathematics should be studied. In the 2000 edition of Baseball Prospectus, Keith Woolner wrote an essay entitled "Baseball's Hilbert Problems."(Kahrl, et al. 2000) Woolner's essay, in the spirit of Hilbert, listed 23 unanswered questions about baseball. If baseball research is now about where David Hilbert was in 1900, football research is about where the Arabs were when they invented algebra. Analysis in football has a long way to go. The football Hilbert Problems do not merely consist of questions that need to be answered. They start with problems collecting the data that would help answer those questions.
In many biometrical applications, the count data encountered often contain extra zeros relative to the Poisson distribution. Zero-inflated Poisson regression models are useful for analyzing such data, but parameter estimates may be seriously biased if the nonzero observations are over-dispersed and simultaneously correlated due to the sampling design or the data collection procedure. In this paper, a zero-inflated negative binomial mixed regression model is presented to analyze a set of pancreas disorder length of stay (LOS) data that comprised mainly same-day separations. Random effects are introduced to account for inter-hospital variations and the dependency of clustered LOS observations. Parameter estimation is achieved by maximizing an appropriate log-likelihood function using an EM algorithm. Alternative modeling strategies, namely the finite mixture of Poisson distributions and the non-parametric maximum likelihood approach, are also considered. The determination of pertinent covariates would assist hospital administrators and clinicians to manage LOS and expenditures efficiently.
Most likely to succeed. The New Yorker. URL http
  • M Gladwell
Gladwell, M. (2008). Most likely to succeed. The New Yorker. URL http://www.